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Entropy 2011, 13(12), 2036-2048; doi:10.3390/e13122036

Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy

Department of Mathematics, National Taiwan Normal University, 88 SEC. 4, Ting Chou Road, Taipei 11677, Taiwan
Received: 31 October 2011 / Revised: 28 November 2011 / Accepted: 12 December 2011 / Published: 20 December 2011
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
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The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound for the gaps of dominant eigenvalues of A and A + V.
Keywords: Kolmogorov-Sinai entropy; Parry’s theorem; Eigenvalue estimates Kolmogorov-Sinai entropy; Parry’s theorem; Eigenvalue estimates
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Shieh, S.-F. Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy. Entropy 2011, 13, 2036-2048.

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